##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Zuhair Mullath

#### University of Massachusetts, Amherst

## Unobstructed Galois deformation problems associated to GSp(4)

##### Abstract:

To a cuspidal automorphic representation of GSp(4) over $\mathbb Q$, one can associate a compatible system of Galois representations $\{\rho_p\}_{p \; \mathrm{prime}}$. For $p$ sufficiently large, the deformation theory of the mod-$p$ reduction $\overline \rho_p$ is expected to be unobstructed -- meaning the universal deformation ring is a power series ring. The global obstructions to deforming $\overline \rho_p$ is controlled by certain adjoint Bloch-Kato Selmer groups, which are expected to be trivial for $p$ large enough. \\ \\ I will talk about some recent results showing that there are no local obstructions to the deformation theory of $\overline \rho_p$ for almost all $p$. \\ \\ This is joint work with M. Broshi, C. Sorensen, and T. Weston.

Host: Kiran Kedlaya

### February 18, 2021

### 1:00 PM

### Location: See https://www.math.ucsd.edu/\~{}nts/

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